Very interesting. Thank you Robert and Martin!
The provisions mentioned in the Constitution can be found in the law https://www.retsinformation.dk/Forms/R0710.aspx?id=45894
A rough translation: § 2
Is there a reason to fear that the thronefollower would be a minor by the time of the death of the King, or for some other reason would be unable to asume the reign, the King - with the approval of the Parliament - makes descision on the conduct of the government via a Regent. If the King dies without such provisions having being made, the council of state immidiately assembles the Parliament to elect a Regent according to the rules in paragraph 1 (Must be a danish citizen of good standing)
(Er der Grund til at frygte, at Thronfølgeren ved Kongens Død vil være umyndig eller af anden Aarsag ude af Stand til strax at tiltræde Regjeringen, træffes der af Kongen med Rigsdagens Samtykke Bestemmelse om Regjeringens Førelse ved en Rigsforstander. Døer Kongen, udenat saadan Bestemmelse er truffen, sammenkalder Statsraadet ufortøvet Rigsdagen, som i en forenet Samling vælger en Rigsforstander efter Reglerne i § 1.)
Previously it has been asmumed that Joachim would become Regent if Christian became king before he became 18. Now one might suspect that this roule would be asumed by Mary.
Is there standing provision for who becomes regent if the monarch is a minor, or is that done on an ad hoc basis?
This is what the Constitution says on the subject:
"Provisions relating to the exercising of sovereign power in the event of the minority, illness, or absence of the King shall be laid down by Statute. Where on the vacancy of the Throne there is no Successor to the Throne, the Parliament shall elect a King and establish the future order of succession to the Throne."